A Units Digit of a Floor

★ 7/10number theory Recursion Modular Arithmetic sequences

Problem

Let

a_n = \left(\sqrt{2} + 1\right)^n - \left(\sqrt{2} - 1\right)^n \qquad (n \in \mathbb{N}^*).

Find the units digit of $\left\lfloor a_{2017} \right\rfloor$ .

Answer

Solution

Difficulty	7/10
Topics	number theory, Recursion, Modular Arithmetic, sequences

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